Growing Half-Balls: Minimizing Storage and Communication Costs in CDNs

Bar-Yehuda, Reuven; Kantor, Erez; Kutten, Shay; Rawitz, Dror

doi:10.1007/978-3-642-31585-5_38

Cited by 5 publications

(7 citation statements)

References 16 publications

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“…where the first and the last inequalities hold by Lemma 3.14 Property (P2) with i and k; the second and the third inequalities hold since u serve l ∈ [v i , v j ]; and the fourth inequality holds by the assumption of case (2). Therefore, in particular, 0 ≤ v k − u serve l ≤ ρ SQ (k).…”

Section: Uncovered Request Has At Least Two Childrenmentioning

confidence: 91%

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Optimal Competitiveness for the Rectilinear Steiner Arborescence Problem

Kantor¹,

Kutten

2015

Automata, Languages, and Programming

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We present optimal online algorithms for two related known problems involving Steiner Arborescence, improving both the lower and the upper bounds. One of them is the well studied continuous problem of the Rectilinear Steiner Arborescence (RSA). We improve the lower bound and the upper bound on the competitive ratio for RSA from O(log N ) and Ω(where N is the number of Steiner points. This separates the competitive ratios of RSA and the Symetric-RSA (SRSA), two problems for which the bounds of Berman and Coulston is STOC 1997 were identical. The second problem is one of the Multimedia Content Distribution problems presented by Papadimitriou et al. in several papers and Charikar et al. SODA 1998. It can be viewed as the discrete counterparts (or a network counterpart) of RSA.For this second problem we present tight bounds also in terms of the network size, in addition to presenting tight bounds in terms of the number of Steiner points (the latter are similar to those we derived for RSA).

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Section: Uncovered Request Has At Least Two Childrenmentioning

confidence: 91%

“…Similarly to e.g. [2,18,20,19,5], at least one copy must remain in the network at all times. be the set of horizontal directed edges of the path from (u, t) to (v, t).…”

Section: Preliminariesmentioning

confidence: 99%

Optimal Competitiveness for the Rectilinear Steiner Arborescence Problem

Kantor¹,

Kutten

2015

Automata, Languages, and Programming

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“…The proof is very similar to that of Ineq. (2). Assume that there exists a level l * such that N R (I l * (v)), t ∈ commit.…”

Section: Analysis Of Line Onmentioning

confidence: 99%

“…A PTAS was presented by [10]. The results of [2] generalized the logarithmic upper bound of online M CD to general networks.…”

Section: Some Additional Related Workmentioning

confidence: 99%

“…Similarly to [1,2,3,12,14,13,5], we assume that the online algorithm may replicate the movie for efficient delivery, but at least one copy of the movie must remain in the network at all times. Alternatively, the system (but not the algorithm) can have the option to delete the movie altogether, this decision is then made known to the online algorithm.…”

Section: Preliminariesmentioning

confidence: 99%

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Optimal Competitiveness for Symmetric Rectilinear Steiner Arborescence and Related Problems

Kantor¹,

Kutten

2014

Automata, Languages, and Programming

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We present optimal competitive algorithms for two interrelated known problems involving Steiner Arborescence. One is the continuous problem of the Symmetric Rectilinear Steiner Arborescence (SRSA), studied by Berman and Coulston as a symmetric version of the known Rectilinear Steiner Arborescence (RSA) problem.A very related, but discrete problem (studied separately in the past) is the online Multimedia Content Delivery (M CD) problem on line networks, presented originally by Papadimitriu, Ramanathan, and Rangan. An efficient content delivery was modeled as a low cost Steiner arborescence in a grid of network×time they defined. We study here the version studied by Charikar, Halperin, and Motwani (who used the same problem definitions, but removed some constraints on the inputs).The bounds on the competitive ratios introduced separately in the above papers are similar for the two problems: O(log N ) for the continuous problem and O(log n) for the network problem, where N was the number of terminals to serve, and n was the size of the network. The lower bounds were Ω( √ log N ) and Ω( √ log n) correspondingly. Berman and Coulston conjectured that both the upper bound and the lower bound could be improved.We disprove this conjecture and close these quadratic gaps for both problems. We first present an O( √ log n) deterministic competitive algorithm for M CD on the line, matching the lower bound. We then translate this algorithm to become a competitive optimal algorithm O( √ log N ) for SRSA. Finally, we translate the latter back to solve M CD problem, this time competitive optimally even in the case that the number of requests is small (that is, O(min{ √ log n, √ log N })). We also present a Ω( 3 √ log n) lower bound on the competitiveness of any randomized algorithm. Some of the techniques may be useful in other contexts. (For example, rather than comparing to the unknown optimum, we compared the costs of the online algorithm to the costs of an approximation offline algorithm).

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